Senate leaders plan to move quickly this month to reject the articles of impeachment against Alejandro N. Mayorkas, the homeland security secretary, setting up a speedy trial in hopes of preventing House Republicans from turning the chamber into a political spectacle.

Senator Chuck Schumer, Democrat of New York and the majority leader, has not yet determined exactly how to go about truncating the proceedings, according to people familiar with the continuing discussions, who spoke on the condition of anonymity to describe plans that were still under development. But he is aiming for quick action, beginning on Feb. 28, the day the House is expected to deliver the charges, that could be over in just a couple of days.

Mr. Schumer still has almost two weeks before House managers plan to formally present senators with the articles of impeachment against Mr. Mayorkas, which the House narrowly approved on Tuesday on a second try after they were defeated the week before. They accuse the secretary of refusing to enforce immigration laws and breaching the public trust regarding the state of the U.S. border with Mexico, effectively declaring President Biden’s immigration policies a constitutional crime.

Senate leaders are betting that there is enough Democratic anger and Republican exasperation at the precedent-breaking nature of the charges — and with the way Mr. Mayorkas’s impeachment was handled — to swiftly exonerate him, either by throwing out the charges entirely or by moving to bring the proceedings to an early close.

And they have no doubt that they would have the votes to acquit him. A conviction would require a two-thirds majority, meaning that at least 18 senators on the Democratic side would have to join Republicans in finding Mr. Mayorkas guilty.

“These charges are a total sham — really shameful — and they deserve absolutely no dignity,” said Senator Richard Blumenthal, Democrat of Connecticut and a member of the Judiciary Committee. “They’re purely a political stunt by the far-right fringe of the MAGA movement and, I think, should be dismissed summarily.”